On a generalised Blaschke-Santal\`o inequality

TL;DR

This paper extends the Blaschke-Santal\

Contribution

It introduces a generalized inequality for convex bodies, providing bounds on dual quermassintegrals of a convex body and its polar, using an inductive approach.

Findings

Establishes a new upper bound for dual quermassintegrals.

Generalizes the classical Blaschke-Santal\

Demonstrates the inequality for convex bodies in R^{n+1}.

Abstract

In this paper, we establish a generalised Blaschke-Santal\`o inequality for convex bodies in $\mathbb R^{n+1}$. This inequality gives an upper bound estimate for the product of dual quermassintegrals of convex body and its polar set. Our argument is based on induction on dimensions.